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A fragmented geometric shape that can be split into parts, each of which approximates a reduced-size copy of the whole, a property which is called self-similarity. Fractals provide the mathematics behind structures in the natural universe—e.g., frost crystals, coastlines, etc.—which cannot be described by the language of euclidean geometry. Fractal analysis is providing new ways to interpret biomedical phenomena. It has been used for classifying histopathology, enzymology, and signal and image compression
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Figure 5 shows the substrate layer distributions in step 2 for those four fractal sets shown previously.
Falconer, The Geometry of Fractal Sets, Cambridge University Press, London, 1985.
The topics are periodic points, chaos in one and two dimensions, systems of differential equations, fractals, creating fractal sets, and complex fractals in Julia sets and the Mandelbrot set.